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<FONT color="green">001</FONT>    /*<a name="line.1"></a>
<FONT color="green">002</FONT>     * Licensed to the Apache Software Foundation (ASF) under one or more<a name="line.2"></a>
<FONT color="green">003</FONT>     * contributor license agreements.  See the NOTICE file distributed with<a name="line.3"></a>
<FONT color="green">004</FONT>     * this work for additional information regarding copyright ownership.<a name="line.4"></a>
<FONT color="green">005</FONT>     * The ASF licenses this file to You under the Apache License, Version 2.0<a name="line.5"></a>
<FONT color="green">006</FONT>     * (the "License"); you may not use this file except in compliance with<a name="line.6"></a>
<FONT color="green">007</FONT>     * the License.  You may obtain a copy of the License at<a name="line.7"></a>
<FONT color="green">008</FONT>     *<a name="line.8"></a>
<FONT color="green">009</FONT>     *      http://www.apache.org/licenses/LICENSE-2.0<a name="line.9"></a>
<FONT color="green">010</FONT>     *<a name="line.10"></a>
<FONT color="green">011</FONT>     * Unless required by applicable law or agreed to in writing, software<a name="line.11"></a>
<FONT color="green">012</FONT>     * distributed under the License is distributed on an "AS IS" BASIS,<a name="line.12"></a>
<FONT color="green">013</FONT>     * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.<a name="line.13"></a>
<FONT color="green">014</FONT>     * See the License for the specific language governing permissions and<a name="line.14"></a>
<FONT color="green">015</FONT>     * limitations under the License.<a name="line.15"></a>
<FONT color="green">016</FONT>     */<a name="line.16"></a>
<FONT color="green">017</FONT>    <a name="line.17"></a>
<FONT color="green">018</FONT>    package org.apache.commons.math.ode.nonstiff;<a name="line.18"></a>
<FONT color="green">019</FONT>    <a name="line.19"></a>
<FONT color="green">020</FONT>    import org.apache.commons.math.ode.DerivativeException;<a name="line.20"></a>
<FONT color="green">021</FONT>    import org.apache.commons.math.ode.FirstOrderDifferentialEquations;<a name="line.21"></a>
<FONT color="green">022</FONT>    import org.apache.commons.math.ode.IntegratorException;<a name="line.22"></a>
<FONT color="green">023</FONT>    import org.apache.commons.math.ode.sampling.AbstractStepInterpolator;<a name="line.23"></a>
<FONT color="green">024</FONT>    import org.apache.commons.math.ode.sampling.DummyStepInterpolator;<a name="line.24"></a>
<FONT color="green">025</FONT>    import org.apache.commons.math.ode.sampling.StepHandler;<a name="line.25"></a>
<FONT color="green">026</FONT>    import org.apache.commons.math.util.FastMath;<a name="line.26"></a>
<FONT color="green">027</FONT>    <a name="line.27"></a>
<FONT color="green">028</FONT>    /**<a name="line.28"></a>
<FONT color="green">029</FONT>     * This class implements the common part of all embedded Runge-Kutta<a name="line.29"></a>
<FONT color="green">030</FONT>     * integrators for Ordinary Differential Equations.<a name="line.30"></a>
<FONT color="green">031</FONT>     *<a name="line.31"></a>
<FONT color="green">032</FONT>     * &lt;p&gt;These methods are embedded explicit Runge-Kutta methods with two<a name="line.32"></a>
<FONT color="green">033</FONT>     * sets of coefficients allowing to estimate the error, their Butcher<a name="line.33"></a>
<FONT color="green">034</FONT>     * arrays are as follows :<a name="line.34"></a>
<FONT color="green">035</FONT>     * &lt;pre&gt;<a name="line.35"></a>
<FONT color="green">036</FONT>     *    0  |<a name="line.36"></a>
<FONT color="green">037</FONT>     *   c2  | a21<a name="line.37"></a>
<FONT color="green">038</FONT>     *   c3  | a31  a32<a name="line.38"></a>
<FONT color="green">039</FONT>     *   ... |        ...<a name="line.39"></a>
<FONT color="green">040</FONT>     *   cs  | as1  as2  ...  ass-1<a name="line.40"></a>
<FONT color="green">041</FONT>     *       |--------------------------<a name="line.41"></a>
<FONT color="green">042</FONT>     *       |  b1   b2  ...   bs-1  bs<a name="line.42"></a>
<FONT color="green">043</FONT>     *       |  b'1  b'2 ...   b's-1 b's<a name="line.43"></a>
<FONT color="green">044</FONT>     * &lt;/pre&gt;<a name="line.44"></a>
<FONT color="green">045</FONT>     * &lt;/p&gt;<a name="line.45"></a>
<FONT color="green">046</FONT>     *<a name="line.46"></a>
<FONT color="green">047</FONT>     * &lt;p&gt;In fact, we rather use the array defined by ej = bj - b'j to<a name="line.47"></a>
<FONT color="green">048</FONT>     * compute directly the error rather than computing two estimates and<a name="line.48"></a>
<FONT color="green">049</FONT>     * then comparing them.&lt;/p&gt;<a name="line.49"></a>
<FONT color="green">050</FONT>     *<a name="line.50"></a>
<FONT color="green">051</FONT>     * &lt;p&gt;Some methods are qualified as &lt;i&gt;fsal&lt;/i&gt; (first same as last)<a name="line.51"></a>
<FONT color="green">052</FONT>     * methods. This means the last evaluation of the derivatives in one<a name="line.52"></a>
<FONT color="green">053</FONT>     * step is the same as the first in the next step. Then, this<a name="line.53"></a>
<FONT color="green">054</FONT>     * evaluation can be reused from one step to the next one and the cost<a name="line.54"></a>
<FONT color="green">055</FONT>     * of such a method is really s-1 evaluations despite the method still<a name="line.55"></a>
<FONT color="green">056</FONT>     * has s stages. This behaviour is true only for successful steps, if<a name="line.56"></a>
<FONT color="green">057</FONT>     * the step is rejected after the error estimation phase, no<a name="line.57"></a>
<FONT color="green">058</FONT>     * evaluation is saved. For an &lt;i&gt;fsal&lt;/i&gt; method, we have cs = 1 and<a name="line.58"></a>
<FONT color="green">059</FONT>     * asi = bi for all i.&lt;/p&gt;<a name="line.59"></a>
<FONT color="green">060</FONT>     *<a name="line.60"></a>
<FONT color="green">061</FONT>     * @version $Revision: 1073158 $ $Date: 2011-02-21 22:46:52 +0100 (lun. 21 f??vr. 2011) $<a name="line.61"></a>
<FONT color="green">062</FONT>     * @since 1.2<a name="line.62"></a>
<FONT color="green">063</FONT>     */<a name="line.63"></a>
<FONT color="green">064</FONT>    <a name="line.64"></a>
<FONT color="green">065</FONT>    public abstract class EmbeddedRungeKuttaIntegrator<a name="line.65"></a>
<FONT color="green">066</FONT>      extends AdaptiveStepsizeIntegrator {<a name="line.66"></a>
<FONT color="green">067</FONT>    <a name="line.67"></a>
<FONT color="green">068</FONT>        /** Indicator for &lt;i&gt;fsal&lt;/i&gt; methods. */<a name="line.68"></a>
<FONT color="green">069</FONT>        private final boolean fsal;<a name="line.69"></a>
<FONT color="green">070</FONT>    <a name="line.70"></a>
<FONT color="green">071</FONT>        /** Time steps from Butcher array (without the first zero). */<a name="line.71"></a>
<FONT color="green">072</FONT>        private final double[] c;<a name="line.72"></a>
<FONT color="green">073</FONT>    <a name="line.73"></a>
<FONT color="green">074</FONT>        /** Internal weights from Butcher array (without the first empty row). */<a name="line.74"></a>
<FONT color="green">075</FONT>        private final double[][] a;<a name="line.75"></a>
<FONT color="green">076</FONT>    <a name="line.76"></a>
<FONT color="green">077</FONT>        /** External weights for the high order method from Butcher array. */<a name="line.77"></a>
<FONT color="green">078</FONT>        private final double[] b;<a name="line.78"></a>
<FONT color="green">079</FONT>    <a name="line.79"></a>
<FONT color="green">080</FONT>        /** Prototype of the step interpolator. */<a name="line.80"></a>
<FONT color="green">081</FONT>        private final RungeKuttaStepInterpolator prototype;<a name="line.81"></a>
<FONT color="green">082</FONT>    <a name="line.82"></a>
<FONT color="green">083</FONT>        /** Stepsize control exponent. */<a name="line.83"></a>
<FONT color="green">084</FONT>        private final double exp;<a name="line.84"></a>
<FONT color="green">085</FONT>    <a name="line.85"></a>
<FONT color="green">086</FONT>        /** Safety factor for stepsize control. */<a name="line.86"></a>
<FONT color="green">087</FONT>        private double safety;<a name="line.87"></a>
<FONT color="green">088</FONT>    <a name="line.88"></a>
<FONT color="green">089</FONT>        /** Minimal reduction factor for stepsize control. */<a name="line.89"></a>
<FONT color="green">090</FONT>        private double minReduction;<a name="line.90"></a>
<FONT color="green">091</FONT>    <a name="line.91"></a>
<FONT color="green">092</FONT>        /** Maximal growth factor for stepsize control. */<a name="line.92"></a>
<FONT color="green">093</FONT>        private double maxGrowth;<a name="line.93"></a>
<FONT color="green">094</FONT>    <a name="line.94"></a>
<FONT color="green">095</FONT>      /** Build a Runge-Kutta integrator with the given Butcher array.<a name="line.95"></a>
<FONT color="green">096</FONT>       * @param name name of the method<a name="line.96"></a>
<FONT color="green">097</FONT>       * @param fsal indicate that the method is an &lt;i&gt;fsal&lt;/i&gt;<a name="line.97"></a>
<FONT color="green">098</FONT>       * @param c time steps from Butcher array (without the first zero)<a name="line.98"></a>
<FONT color="green">099</FONT>       * @param a internal weights from Butcher array (without the first empty row)<a name="line.99"></a>
<FONT color="green">100</FONT>       * @param b propagation weights for the high order method from Butcher array<a name="line.100"></a>
<FONT color="green">101</FONT>       * @param prototype prototype of the step interpolator to use<a name="line.101"></a>
<FONT color="green">102</FONT>       * @param minStep minimal step (must be positive even for backward<a name="line.102"></a>
<FONT color="green">103</FONT>       * integration), the last step can be smaller than this<a name="line.103"></a>
<FONT color="green">104</FONT>       * @param maxStep maximal step (must be positive even for backward<a name="line.104"></a>
<FONT color="green">105</FONT>       * integration)<a name="line.105"></a>
<FONT color="green">106</FONT>       * @param scalAbsoluteTolerance allowed absolute error<a name="line.106"></a>
<FONT color="green">107</FONT>       * @param scalRelativeTolerance allowed relative error<a name="line.107"></a>
<FONT color="green">108</FONT>       */<a name="line.108"></a>
<FONT color="green">109</FONT>      protected EmbeddedRungeKuttaIntegrator(final String name, final boolean fsal,<a name="line.109"></a>
<FONT color="green">110</FONT>                                             final double[] c, final double[][] a, final double[] b,<a name="line.110"></a>
<FONT color="green">111</FONT>                                             final RungeKuttaStepInterpolator prototype,<a name="line.111"></a>
<FONT color="green">112</FONT>                                             final double minStep, final double maxStep,<a name="line.112"></a>
<FONT color="green">113</FONT>                                             final double scalAbsoluteTolerance,<a name="line.113"></a>
<FONT color="green">114</FONT>                                             final double scalRelativeTolerance) {<a name="line.114"></a>
<FONT color="green">115</FONT>    <a name="line.115"></a>
<FONT color="green">116</FONT>        super(name, minStep, maxStep, scalAbsoluteTolerance, scalRelativeTolerance);<a name="line.116"></a>
<FONT color="green">117</FONT>    <a name="line.117"></a>
<FONT color="green">118</FONT>        this.fsal      = fsal;<a name="line.118"></a>
<FONT color="green">119</FONT>        this.c         = c;<a name="line.119"></a>
<FONT color="green">120</FONT>        this.a         = a;<a name="line.120"></a>
<FONT color="green">121</FONT>        this.b         = b;<a name="line.121"></a>
<FONT color="green">122</FONT>        this.prototype = prototype;<a name="line.122"></a>
<FONT color="green">123</FONT>    <a name="line.123"></a>
<FONT color="green">124</FONT>        exp = -1.0 / getOrder();<a name="line.124"></a>
<FONT color="green">125</FONT>    <a name="line.125"></a>
<FONT color="green">126</FONT>        // set the default values of the algorithm control parameters<a name="line.126"></a>
<FONT color="green">127</FONT>        setSafety(0.9);<a name="line.127"></a>
<FONT color="green">128</FONT>        setMinReduction(0.2);<a name="line.128"></a>
<FONT color="green">129</FONT>        setMaxGrowth(10.0);<a name="line.129"></a>
<FONT color="green">130</FONT>    <a name="line.130"></a>
<FONT color="green">131</FONT>      }<a name="line.131"></a>
<FONT color="green">132</FONT>    <a name="line.132"></a>
<FONT color="green">133</FONT>      /** Build a Runge-Kutta integrator with the given Butcher array.<a name="line.133"></a>
<FONT color="green">134</FONT>       * @param name name of the method<a name="line.134"></a>
<FONT color="green">135</FONT>       * @param fsal indicate that the method is an &lt;i&gt;fsal&lt;/i&gt;<a name="line.135"></a>
<FONT color="green">136</FONT>       * @param c time steps from Butcher array (without the first zero)<a name="line.136"></a>
<FONT color="green">137</FONT>       * @param a internal weights from Butcher array (without the first empty row)<a name="line.137"></a>
<FONT color="green">138</FONT>       * @param b propagation weights for the high order method from Butcher array<a name="line.138"></a>
<FONT color="green">139</FONT>       * @param prototype prototype of the step interpolator to use<a name="line.139"></a>
<FONT color="green">140</FONT>       * @param minStep minimal step (must be positive even for backward<a name="line.140"></a>
<FONT color="green">141</FONT>       * integration), the last step can be smaller than this<a name="line.141"></a>
<FONT color="green">142</FONT>       * @param maxStep maximal step (must be positive even for backward<a name="line.142"></a>
<FONT color="green">143</FONT>       * integration)<a name="line.143"></a>
<FONT color="green">144</FONT>       * @param vecAbsoluteTolerance allowed absolute error<a name="line.144"></a>
<FONT color="green">145</FONT>       * @param vecRelativeTolerance allowed relative error<a name="line.145"></a>
<FONT color="green">146</FONT>       */<a name="line.146"></a>
<FONT color="green">147</FONT>      protected EmbeddedRungeKuttaIntegrator(final String name, final boolean fsal,<a name="line.147"></a>
<FONT color="green">148</FONT>                                             final double[] c, final double[][] a, final double[] b,<a name="line.148"></a>
<FONT color="green">149</FONT>                                             final RungeKuttaStepInterpolator prototype,<a name="line.149"></a>
<FONT color="green">150</FONT>                                             final double   minStep, final double maxStep,<a name="line.150"></a>
<FONT color="green">151</FONT>                                             final double[] vecAbsoluteTolerance,<a name="line.151"></a>
<FONT color="green">152</FONT>                                             final double[] vecRelativeTolerance) {<a name="line.152"></a>
<FONT color="green">153</FONT>    <a name="line.153"></a>
<FONT color="green">154</FONT>        super(name, minStep, maxStep, vecAbsoluteTolerance, vecRelativeTolerance);<a name="line.154"></a>
<FONT color="green">155</FONT>    <a name="line.155"></a>
<FONT color="green">156</FONT>        this.fsal      = fsal;<a name="line.156"></a>
<FONT color="green">157</FONT>        this.c         = c;<a name="line.157"></a>
<FONT color="green">158</FONT>        this.a         = a;<a name="line.158"></a>
<FONT color="green">159</FONT>        this.b         = b;<a name="line.159"></a>
<FONT color="green">160</FONT>        this.prototype = prototype;<a name="line.160"></a>
<FONT color="green">161</FONT>    <a name="line.161"></a>
<FONT color="green">162</FONT>        exp = -1.0 / getOrder();<a name="line.162"></a>
<FONT color="green">163</FONT>    <a name="line.163"></a>
<FONT color="green">164</FONT>        // set the default values of the algorithm control parameters<a name="line.164"></a>
<FONT color="green">165</FONT>        setSafety(0.9);<a name="line.165"></a>
<FONT color="green">166</FONT>        setMinReduction(0.2);<a name="line.166"></a>
<FONT color="green">167</FONT>        setMaxGrowth(10.0);<a name="line.167"></a>
<FONT color="green">168</FONT>    <a name="line.168"></a>
<FONT color="green">169</FONT>      }<a name="line.169"></a>
<FONT color="green">170</FONT>    <a name="line.170"></a>
<FONT color="green">171</FONT>      /** Get the order of the method.<a name="line.171"></a>
<FONT color="green">172</FONT>       * @return order of the method<a name="line.172"></a>
<FONT color="green">173</FONT>       */<a name="line.173"></a>
<FONT color="green">174</FONT>      public abstract int getOrder();<a name="line.174"></a>
<FONT color="green">175</FONT>    <a name="line.175"></a>
<FONT color="green">176</FONT>      /** Get the safety factor for stepsize control.<a name="line.176"></a>
<FONT color="green">177</FONT>       * @return safety factor<a name="line.177"></a>
<FONT color="green">178</FONT>       */<a name="line.178"></a>
<FONT color="green">179</FONT>      public double getSafety() {<a name="line.179"></a>
<FONT color="green">180</FONT>        return safety;<a name="line.180"></a>
<FONT color="green">181</FONT>      }<a name="line.181"></a>
<FONT color="green">182</FONT>    <a name="line.182"></a>
<FONT color="green">183</FONT>      /** Set the safety factor for stepsize control.<a name="line.183"></a>
<FONT color="green">184</FONT>       * @param safety safety factor<a name="line.184"></a>
<FONT color="green">185</FONT>       */<a name="line.185"></a>
<FONT color="green">186</FONT>      public void setSafety(final double safety) {<a name="line.186"></a>
<FONT color="green">187</FONT>        this.safety = safety;<a name="line.187"></a>
<FONT color="green">188</FONT>      }<a name="line.188"></a>
<FONT color="green">189</FONT>    <a name="line.189"></a>
<FONT color="green">190</FONT>      /** {@inheritDoc} */<a name="line.190"></a>
<FONT color="green">191</FONT>      @Override<a name="line.191"></a>
<FONT color="green">192</FONT>      public double integrate(final FirstOrderDifferentialEquations equations,<a name="line.192"></a>
<FONT color="green">193</FONT>                              final double t0, final double[] y0,<a name="line.193"></a>
<FONT color="green">194</FONT>                              final double t, final double[] y)<a name="line.194"></a>
<FONT color="green">195</FONT>      throws DerivativeException, IntegratorException {<a name="line.195"></a>
<FONT color="green">196</FONT>    <a name="line.196"></a>
<FONT color="green">197</FONT>        sanityChecks(equations, t0, y0, t, y);<a name="line.197"></a>
<FONT color="green">198</FONT>        setEquations(equations);<a name="line.198"></a>
<FONT color="green">199</FONT>        resetEvaluations();<a name="line.199"></a>
<FONT color="green">200</FONT>        final boolean forward = t &gt; t0;<a name="line.200"></a>
<FONT color="green">201</FONT>    <a name="line.201"></a>
<FONT color="green">202</FONT>        // create some internal working arrays<a name="line.202"></a>
<FONT color="green">203</FONT>        final int stages = c.length + 1;<a name="line.203"></a>
<FONT color="green">204</FONT>        if (y != y0) {<a name="line.204"></a>
<FONT color="green">205</FONT>          System.arraycopy(y0, 0, y, 0, y0.length);<a name="line.205"></a>
<FONT color="green">206</FONT>        }<a name="line.206"></a>
<FONT color="green">207</FONT>        final double[][] yDotK = new double[stages][y0.length];<a name="line.207"></a>
<FONT color="green">208</FONT>        final double[] yTmp    = new double[y0.length];<a name="line.208"></a>
<FONT color="green">209</FONT>        final double[] yDotTmp = new double[y0.length];<a name="line.209"></a>
<FONT color="green">210</FONT>    <a name="line.210"></a>
<FONT color="green">211</FONT>        // set up an interpolator sharing the integrator arrays<a name="line.211"></a>
<FONT color="green">212</FONT>        AbstractStepInterpolator interpolator;<a name="line.212"></a>
<FONT color="green">213</FONT>        if (requiresDenseOutput()) {<a name="line.213"></a>
<FONT color="green">214</FONT>          final RungeKuttaStepInterpolator rki = (RungeKuttaStepInterpolator) prototype.copy();<a name="line.214"></a>
<FONT color="green">215</FONT>          rki.reinitialize(this, yTmp, yDotK, forward);<a name="line.215"></a>
<FONT color="green">216</FONT>          interpolator = rki;<a name="line.216"></a>
<FONT color="green">217</FONT>        } else {<a name="line.217"></a>
<FONT color="green">218</FONT>          interpolator = new DummyStepInterpolator(yTmp, yDotK[stages - 1], forward);<a name="line.218"></a>
<FONT color="green">219</FONT>        }<a name="line.219"></a>
<FONT color="green">220</FONT>        interpolator.storeTime(t0);<a name="line.220"></a>
<FONT color="green">221</FONT>    <a name="line.221"></a>
<FONT color="green">222</FONT>        // set up integration control objects<a name="line.222"></a>
<FONT color="green">223</FONT>        stepStart         = t0;<a name="line.223"></a>
<FONT color="green">224</FONT>        double  hNew      = 0;<a name="line.224"></a>
<FONT color="green">225</FONT>        boolean firstTime = true;<a name="line.225"></a>
<FONT color="green">226</FONT>        for (StepHandler handler : stepHandlers) {<a name="line.226"></a>
<FONT color="green">227</FONT>            handler.reset();<a name="line.227"></a>
<FONT color="green">228</FONT>        }<a name="line.228"></a>
<FONT color="green">229</FONT>        setStateInitialized(false);<a name="line.229"></a>
<FONT color="green">230</FONT>    <a name="line.230"></a>
<FONT color="green">231</FONT>        // main integration loop<a name="line.231"></a>
<FONT color="green">232</FONT>        isLastStep = false;<a name="line.232"></a>
<FONT color="green">233</FONT>        do {<a name="line.233"></a>
<FONT color="green">234</FONT>    <a name="line.234"></a>
<FONT color="green">235</FONT>          interpolator.shift();<a name="line.235"></a>
<FONT color="green">236</FONT>    <a name="line.236"></a>
<FONT color="green">237</FONT>          // iterate over step size, ensuring local normalized error is smaller than 1<a name="line.237"></a>
<FONT color="green">238</FONT>          double error = 10;<a name="line.238"></a>
<FONT color="green">239</FONT>          while (error &gt;= 1.0) {<a name="line.239"></a>
<FONT color="green">240</FONT>    <a name="line.240"></a>
<FONT color="green">241</FONT>            if (firstTime || !fsal) {<a name="line.241"></a>
<FONT color="green">242</FONT>              // first stage<a name="line.242"></a>
<FONT color="green">243</FONT>              computeDerivatives(stepStart, y, yDotK[0]);<a name="line.243"></a>
<FONT color="green">244</FONT>            }<a name="line.244"></a>
<FONT color="green">245</FONT>    <a name="line.245"></a>
<FONT color="green">246</FONT>            if (firstTime) {<a name="line.246"></a>
<FONT color="green">247</FONT>              final double[] scale = new double[mainSetDimension];<a name="line.247"></a>
<FONT color="green">248</FONT>              if (vecAbsoluteTolerance == null) {<a name="line.248"></a>
<FONT color="green">249</FONT>                  for (int i = 0; i &lt; scale.length; ++i) {<a name="line.249"></a>
<FONT color="green">250</FONT>                    scale[i] = scalAbsoluteTolerance + scalRelativeTolerance * FastMath.abs(y[i]);<a name="line.250"></a>
<FONT color="green">251</FONT>                  }<a name="line.251"></a>
<FONT color="green">252</FONT>              } else {<a name="line.252"></a>
<FONT color="green">253</FONT>                  for (int i = 0; i &lt; scale.length; ++i) {<a name="line.253"></a>
<FONT color="green">254</FONT>                    scale[i] = vecAbsoluteTolerance[i] + vecRelativeTolerance[i] * FastMath.abs(y[i]);<a name="line.254"></a>
<FONT color="green">255</FONT>                  }<a name="line.255"></a>
<FONT color="green">256</FONT>              }<a name="line.256"></a>
<FONT color="green">257</FONT>              hNew = initializeStep(equations, forward, getOrder(), scale,<a name="line.257"></a>
<FONT color="green">258</FONT>                                    stepStart, y, yDotK[0], yTmp, yDotK[1]);<a name="line.258"></a>
<FONT color="green">259</FONT>              firstTime = false;<a name="line.259"></a>
<FONT color="green">260</FONT>            }<a name="line.260"></a>
<FONT color="green">261</FONT>    <a name="line.261"></a>
<FONT color="green">262</FONT>            stepSize = hNew;<a name="line.262"></a>
<FONT color="green">263</FONT>    <a name="line.263"></a>
<FONT color="green">264</FONT>            // next stages<a name="line.264"></a>
<FONT color="green">265</FONT>            for (int k = 1; k &lt; stages; ++k) {<a name="line.265"></a>
<FONT color="green">266</FONT>    <a name="line.266"></a>
<FONT color="green">267</FONT>              for (int j = 0; j &lt; y0.length; ++j) {<a name="line.267"></a>
<FONT color="green">268</FONT>                double sum = a[k-1][0] * yDotK[0][j];<a name="line.268"></a>
<FONT color="green">269</FONT>                for (int l = 1; l &lt; k; ++l) {<a name="line.269"></a>
<FONT color="green">270</FONT>                  sum += a[k-1][l] * yDotK[l][j];<a name="line.270"></a>
<FONT color="green">271</FONT>                }<a name="line.271"></a>
<FONT color="green">272</FONT>                yTmp[j] = y[j] + stepSize * sum;<a name="line.272"></a>
<FONT color="green">273</FONT>              }<a name="line.273"></a>
<FONT color="green">274</FONT>    <a name="line.274"></a>
<FONT color="green">275</FONT>              computeDerivatives(stepStart + c[k-1] * stepSize, yTmp, yDotK[k]);<a name="line.275"></a>
<FONT color="green">276</FONT>    <a name="line.276"></a>
<FONT color="green">277</FONT>            }<a name="line.277"></a>
<FONT color="green">278</FONT>    <a name="line.278"></a>
<FONT color="green">279</FONT>            // estimate the state at the end of the step<a name="line.279"></a>
<FONT color="green">280</FONT>            for (int j = 0; j &lt; y0.length; ++j) {<a name="line.280"></a>
<FONT color="green">281</FONT>              double sum    = b[0] * yDotK[0][j];<a name="line.281"></a>
<FONT color="green">282</FONT>              for (int l = 1; l &lt; stages; ++l) {<a name="line.282"></a>
<FONT color="green">283</FONT>                sum    += b[l] * yDotK[l][j];<a name="line.283"></a>
<FONT color="green">284</FONT>              }<a name="line.284"></a>
<FONT color="green">285</FONT>              yTmp[j] = y[j] + stepSize * sum;<a name="line.285"></a>
<FONT color="green">286</FONT>            }<a name="line.286"></a>
<FONT color="green">287</FONT>    <a name="line.287"></a>
<FONT color="green">288</FONT>            // estimate the error at the end of the step<a name="line.288"></a>
<FONT color="green">289</FONT>            error = estimateError(yDotK, y, yTmp, stepSize);<a name="line.289"></a>
<FONT color="green">290</FONT>            if (error &gt;= 1.0) {<a name="line.290"></a>
<FONT color="green">291</FONT>              // reject the step and attempt to reduce error by stepsize control<a name="line.291"></a>
<FONT color="green">292</FONT>              final double factor =<a name="line.292"></a>
<FONT color="green">293</FONT>                  FastMath.min(maxGrowth,<a name="line.293"></a>
<FONT color="green">294</FONT>                               FastMath.max(minReduction, safety * FastMath.pow(error, exp)));<a name="line.294"></a>
<FONT color="green">295</FONT>              hNew = filterStep(stepSize * factor, forward, false);<a name="line.295"></a>
<FONT color="green">296</FONT>            }<a name="line.296"></a>
<FONT color="green">297</FONT>    <a name="line.297"></a>
<FONT color="green">298</FONT>          }<a name="line.298"></a>
<FONT color="green">299</FONT>    <a name="line.299"></a>
<FONT color="green">300</FONT>          // local error is small enough: accept the step, trigger events and step handlers<a name="line.300"></a>
<FONT color="green">301</FONT>          interpolator.storeTime(stepStart + stepSize);<a name="line.301"></a>
<FONT color="green">302</FONT>          System.arraycopy(yTmp, 0, y, 0, y0.length);<a name="line.302"></a>
<FONT color="green">303</FONT>          System.arraycopy(yDotK[stages - 1], 0, yDotTmp, 0, y0.length);<a name="line.303"></a>
<FONT color="green">304</FONT>          stepStart = acceptStep(interpolator, y, yDotTmp, t);<a name="line.304"></a>
<FONT color="green">305</FONT>    <a name="line.305"></a>
<FONT color="green">306</FONT>          if (!isLastStep) {<a name="line.306"></a>
<FONT color="green">307</FONT>    <a name="line.307"></a>
<FONT color="green">308</FONT>              // prepare next step<a name="line.308"></a>
<FONT color="green">309</FONT>              interpolator.storeTime(stepStart);<a name="line.309"></a>
<FONT color="green">310</FONT>    <a name="line.310"></a>
<FONT color="green">311</FONT>              if (fsal) {<a name="line.311"></a>
<FONT color="green">312</FONT>                  // save the last evaluation for the next step<a name="line.312"></a>
<FONT color="green">313</FONT>                  System.arraycopy(yDotTmp, 0, yDotK[0], 0, y0.length);<a name="line.313"></a>
<FONT color="green">314</FONT>              }<a name="line.314"></a>
<FONT color="green">315</FONT>    <a name="line.315"></a>
<FONT color="green">316</FONT>              // stepsize control for next step<a name="line.316"></a>
<FONT color="green">317</FONT>              final double factor =<a name="line.317"></a>
<FONT color="green">318</FONT>                  FastMath.min(maxGrowth, FastMath.max(minReduction, safety * FastMath.pow(error, exp)));<a name="line.318"></a>
<FONT color="green">319</FONT>              final double  scaledH    = stepSize * factor;<a name="line.319"></a>
<FONT color="green">320</FONT>              final double  nextT      = stepStart + scaledH;<a name="line.320"></a>
<FONT color="green">321</FONT>              final boolean nextIsLast = forward ? (nextT &gt;= t) : (nextT &lt;= t);<a name="line.321"></a>
<FONT color="green">322</FONT>              hNew = filterStep(scaledH, forward, nextIsLast);<a name="line.322"></a>
<FONT color="green">323</FONT>    <a name="line.323"></a>
<FONT color="green">324</FONT>              final double  filteredNextT      = stepStart + hNew;<a name="line.324"></a>
<FONT color="green">325</FONT>              final boolean filteredNextIsLast = forward ? (filteredNextT &gt;= t) : (filteredNextT &lt;= t);<a name="line.325"></a>
<FONT color="green">326</FONT>              if (filteredNextIsLast) {<a name="line.326"></a>
<FONT color="green">327</FONT>                  hNew = t - stepStart;<a name="line.327"></a>
<FONT color="green">328</FONT>              }<a name="line.328"></a>
<FONT color="green">329</FONT>    <a name="line.329"></a>
<FONT color="green">330</FONT>          }<a name="line.330"></a>
<FONT color="green">331</FONT>    <a name="line.331"></a>
<FONT color="green">332</FONT>        } while (!isLastStep);<a name="line.332"></a>
<FONT color="green">333</FONT>    <a name="line.333"></a>
<FONT color="green">334</FONT>        final double stopTime = stepStart;<a name="line.334"></a>
<FONT color="green">335</FONT>        resetInternalState();<a name="line.335"></a>
<FONT color="green">336</FONT>        return stopTime;<a name="line.336"></a>
<FONT color="green">337</FONT>    <a name="line.337"></a>
<FONT color="green">338</FONT>      }<a name="line.338"></a>
<FONT color="green">339</FONT>    <a name="line.339"></a>
<FONT color="green">340</FONT>      /** Get the minimal reduction factor for stepsize control.<a name="line.340"></a>
<FONT color="green">341</FONT>       * @return minimal reduction factor<a name="line.341"></a>
<FONT color="green">342</FONT>       */<a name="line.342"></a>
<FONT color="green">343</FONT>      public double getMinReduction() {<a name="line.343"></a>
<FONT color="green">344</FONT>        return minReduction;<a name="line.344"></a>
<FONT color="green">345</FONT>      }<a name="line.345"></a>
<FONT color="green">346</FONT>    <a name="line.346"></a>
<FONT color="green">347</FONT>      /** Set the minimal reduction factor for stepsize control.<a name="line.347"></a>
<FONT color="green">348</FONT>       * @param minReduction minimal reduction factor<a name="line.348"></a>
<FONT color="green">349</FONT>       */<a name="line.349"></a>
<FONT color="green">350</FONT>      public void setMinReduction(final double minReduction) {<a name="line.350"></a>
<FONT color="green">351</FONT>        this.minReduction = minReduction;<a name="line.351"></a>
<FONT color="green">352</FONT>      }<a name="line.352"></a>
<FONT color="green">353</FONT>    <a name="line.353"></a>
<FONT color="green">354</FONT>      /** Get the maximal growth factor for stepsize control.<a name="line.354"></a>
<FONT color="green">355</FONT>       * @return maximal growth factor<a name="line.355"></a>
<FONT color="green">356</FONT>       */<a name="line.356"></a>
<FONT color="green">357</FONT>      public double getMaxGrowth() {<a name="line.357"></a>
<FONT color="green">358</FONT>        return maxGrowth;<a name="line.358"></a>
<FONT color="green">359</FONT>      }<a name="line.359"></a>
<FONT color="green">360</FONT>    <a name="line.360"></a>
<FONT color="green">361</FONT>      /** Set the maximal growth factor for stepsize control.<a name="line.361"></a>
<FONT color="green">362</FONT>       * @param maxGrowth maximal growth factor<a name="line.362"></a>
<FONT color="green">363</FONT>       */<a name="line.363"></a>
<FONT color="green">364</FONT>      public void setMaxGrowth(final double maxGrowth) {<a name="line.364"></a>
<FONT color="green">365</FONT>        this.maxGrowth = maxGrowth;<a name="line.365"></a>
<FONT color="green">366</FONT>      }<a name="line.366"></a>
<FONT color="green">367</FONT>    <a name="line.367"></a>
<FONT color="green">368</FONT>      /** Compute the error ratio.<a name="line.368"></a>
<FONT color="green">369</FONT>       * @param yDotK derivatives computed during the first stages<a name="line.369"></a>
<FONT color="green">370</FONT>       * @param y0 estimate of the step at the start of the step<a name="line.370"></a>
<FONT color="green">371</FONT>       * @param y1 estimate of the step at the end of the step<a name="line.371"></a>
<FONT color="green">372</FONT>       * @param h  current step<a name="line.372"></a>
<FONT color="green">373</FONT>       * @return error ratio, greater than 1 if step should be rejected<a name="line.373"></a>
<FONT color="green">374</FONT>       */<a name="line.374"></a>
<FONT color="green">375</FONT>      protected abstract double estimateError(double[][] yDotK,<a name="line.375"></a>
<FONT color="green">376</FONT>                                              double[] y0, double[] y1,<a name="line.376"></a>
<FONT color="green">377</FONT>                                              double h);<a name="line.377"></a>
<FONT color="green">378</FONT>    <a name="line.378"></a>
<FONT color="green">379</FONT>    }<a name="line.379"></a>




























































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